The violent end of some stellar objects, a supernova (SN) explosion, is the beginning of an incredible sequence of energy injection in the surrounding interstellar medium (ISM). A SN explosion ejects material with mass ranging from \(\sim \) 1.4 to \(\sim \) 20 \(M_\odot \)  and a typical energy of 10\(^{50-52}\)  ergs (see e.g. [1]}) and drives fast shock waves, about 10\(^4\)  km s\(^{-1}\)  ahead of the ejecta (the expelled stellar material) through the interstellar medium. Already at early stages, SNe play a crucial, multifaceted role in the evolution of galaxies. The explosion and subsequent dispersion of matter is itself the most important source of elements heavier than nitrogen in the gas phase [2]}. The fast shocks inject kinetic energy that gradually decays in turbulence, a key process in the regulation of star formation on galactic scales [3]}. The fast shock fronts are also a recognized site for the production of the bulk of cosmic rays (CRs, at least at GeV energies; see e.g. [4]}, [5]} and references therein for recent reviews), although alternative origins draw more and more attention (such as superbubbles and Fermi bubbles, see e.g. [6]}, [7]} and references therein for recent reviews). Finally, the hot (10\(^6 - 10^8\)  K) and relatively dense (\(1-10\)  cm\(^{-3}\) ) conditions in the ejecta could be favourable to the synthesis of cosmic dust up to hundred years after the explosion (see recent reviews by [8]}, [9]}, [10]}). After the first phases of expansion (free, then adiabatic), the temperature of the shock front drops to 10\(^6\)  K, allowing the gas to radiatively cool down. At this stage, the so-called supernova remnant (SNR) resembles a spherical shell of \(10-20\)  pc radius, delimitated by regions where shocks interact with the ambient medium.
